Performance Limits of Score-Based Generative Models via Stochastic Thermodynamics

We connect score-based generative models and stochastic thermodynamics by deriving performance limits expressed in terms of entropy rates. Our main theoretical result is a lower bound on the negative log-likelihood that relates model accuracy to the entropy rates induced by the learned score and the entropies of the data and noise distributions. We numerically validate the lower bound and show that improved model accuracy is accompanied by increased entropy production, revealing an explicit accuracy–dissipation tradeoff. Finally, we use the lower bound to estimate the differential entropy of data directly from the trained score network. Together, these results provide physically interpretable limits, practical empirical probes, and a unified theoretical framework linking generative modeling to fundamental principles of stochastic thermodynamics, with implications for controllable generative modeling and emerging computing hardware.